What is (\partial)/(\partial y)(e^{yx}y^2) ?

The answer to (\partial)/(\partial y)(e^{yx}y^2) is e^{yx}xy^2+2ye^{yx}

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(\partial)/(\partial y)(e^{yx}y^2)

\frac{\partial}{\partial y} (e^{y x} y^{2})

e^{y x} x y^{2} + 2 y e^{y x}

Solution steps

\frac{\partial}{\partial y} (e^{y x} y^{2})

Treat

x

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{y x}, g = y^{2}

= \frac{\partial}{\partial y} (e^{y x}) y^{2} + \frac{\partial}{\partial y} (y^{2}) e^{y x}

\frac{\partial}{\partial y} (e^{y x}) = e^{y x} x

\frac{\partial}{\partial y} (y^{2}) = 2 y

= e^{y x} x y^{2} + 2 y e^{y x}

f (x) = (x - 4) (x^{2} + 8)

y^{^{'}} = 4 y + y^{4}

\frac{d}{d x} (\frac{x ^{2} - 9 x + 14}{( x - 5 ) ( x - 10 )})

\frac{\partial}{\partial x} (y x^{- 1})

\frac{( x ^{2} + 1 ) d y}{d x} + 6 x (y - 1) = 0, y (0) = 6

What is (\partial)/(\partial y)(e^{yx}y^2) ?
The answer to (\partial)/(\partial y)(e^{yx}y^2) is e^{yx}xy^2+2ye^{yx}